# Solve $Mx = 0$ for $x$

Given an $m$ by $n$ matrix $M$ whose elements are $0$ or $1$, is there an efficient way of finding a vector $x \ne 0$ whose are elements are from $-1,0,1$ such that $Mx = 0$, or even determining if one exists?

• This seems to be a difficult problem... One possibility: solve the polynomial system given by the linear equations $M\cdot x=0$ and by the equations $x_i^3-x_i=0$.
– emeu
Dec 19 '13 at 19:22
• You mean $x \ne 0$, right? Dec 20 '13 at 12:29
• @ronno Thank you for that fix. Dec 20 '13 at 18:08